Question

Find sets A, B and C such that $A\cap B,A\cap C\mathrm{and}B\cap C$ are non-empty sets and $A\cap B\cap C=\varphi$.

Answer 1

Let us consider the following sets,

A = {5, 6, 10 }
B = {6,8,9}
C = {9,10,11}

$$\begin{gathered} \mathrm{Clearly},A\cap B=\left\{6\right\} \\ B\cap C=\left\{9\right\},A\cap C=\left\{10\right\}\mathrm{and}\mathrm{A}\cap \mathrm{B}\cap \mathrm{C}=\mathrm{\varphi } \\ \mathrm{It}\mathrm{means}\mathrm{that},A\cap B,B\cap C\mathrm{and}A\cap C\mathrm{are}\mathrm{non}\mathrm{empty}\mathrm{sets} \\ \mathrm{and}\mathrm{A}\cap \mathrm{B}\cap \mathrm{C}=\mathrm{\varphi } \end{gathered}$$